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By Sri Harsha Garapati MS Mechanical Engineering University of South Florida

Analysis of Single Fiber Pushout Test of Fiber Reinforced Composite with a Nonhomogeneous Interphase. By Sri Harsha Garapati MS Mechanical Engineering University of South Florida Major Professor: Autar Kaw, Ph. D. Committee: Glen Besterfield, Ph. D. Craig Lusk, Ph. D. Objective.

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By Sri Harsha Garapati MS Mechanical Engineering University of South Florida

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  1. Analysis of Single Fiber Pushout Test of Fiber Reinforced Composite with a Nonhomogeneous Interphase By Sri Harsha Garapati MS Mechanical Engineering University of South Florida Major Professor: Autar Kaw, Ph. D. Committee: Glen Besterfield, Ph. D. Craig Lusk, Ph. D. Sri Harsha Garapati

  2. Objective • Modeling a finite element model of fiber reinforced composite with nonhomogeneous interphase • To analyze the effects of critical parameters on the results of single fiber pushout test • To perform a qualitative and quantitative study of these parameters on the results of single fiber pushout test. Sri Harsha Garapati

  3. Outline • Single Fiber Pushout Test • Literature Review • Formulation • Finite Element Modeling and Validation • Results and Conclusions Sri Harsha Garapati

  4. Single Fiber Pushout Test • The fiber in the specimen is pushed out by the indenter and the interfacial properties are extracted from the load- displacement curve. Sri Harsha Garapati

  5. Literature Review • Analytical Models • Shear Lag Models • Boundary Element Method • Finite Element Models Sri Harsha Garapati

  6. Interphase • In polymeric matrix composites, the interphase is formed due to chemical reaction between the fiber and the matrix • It is sometimes introduced voluntarily to improve the fracture toughness Sri Harsha Garapati

  7. Nonhomogeneous Interphase • Interphase might have multiple regions of chemically distinct layers • Functionally graded interphases are nonhomogeneous Sri Harsha Garapati

  8. Formulation • Geometry • Properties • Continuity Equations • Boundary Conditions Sri Harsha Garapati

  9. Geometry Sri Harsha Garapati

  10. Properties • Properties of fiber and matrix are taken from the literature • Interphase properties • Properties of the composite are found by using recursive concentric cylinder model developed by Sutcu (1992) • Sutcu, M., 1992, "Recursive Concentric Cylinder Model for Composites Containing Coated Fibers," International Journal of Solids and Structures, 29(2) pp. 197. Sri Harsha Garapati

  11. Variation of Elastic Moduli in the Interphase Exponential Linear Sri Harsha Garapati

  12. Continuity Equations • Radial and axial displacements should be the same at all the interfaces • Radial and shear stresses should be the same at all the interfaces Sri Harsha Garapati

  13. Boundary Conditions BC-1 BC-2 Sri Harsha Garapati

  14. Factors for Sensitivity Analysis • Type of Indenter (Spherical, Uniform, Flat) • Fiber Volume Fraction • Thickness of Interphase to Radius of Fiber Ratio (TIRFR) • Type of Interphase (Linear, Exponential) • Boundary Conditions (BC-1, BC-2) Sri Harsha Garapati

  15. Responses for Sensitivity Analysis • Load to Contact Depth Ratio (LCDR) • Normalized Maximum Interfacial Radial Stress (NMIRS) • Normalized Maximum Interfacial Shear Stress (NMISS) Sri Harsha Garapati

  16. Loading Flat indenter loading Spherical indenter loading Uniform pressure indenter loading Sri Harsha Garapati

  17. Finite Element Modeling Sri Harsha Garapati

  18. Contact Elements at the Interfaces Sri Harsha Garapati

  19. Sri Harsha Garapati

  20. Contact Radius Fischer-Cripps, A. C., 1999, "The Hertzian Contact Surface“, Journal of Materials Science, 34(1) pp. 129. Sri Harsha Garapati

  21. Verification of Bonded Contact • Interfacial radial and shear stresses on either side of all the interfaces are observed and they differ by less than 1%. • The displacements (both radial and axial) on either side of all the interfaces are found to be the with in 0.1% Sri Harsha Garapati

  22. Validation Spherical indenter Flat indenter Uniform indenter Sri Harsha Garapati

  23. Validation of the Interfacial Stresses Typical distribution of normalized interfacial shear stress Typical distribution of normalized interfacial radial stress Sri Harsha Garapati

  24. Convergence Test Sri Harsha Garapati

  25. Comparison with Huang’s Shear-Lag Model Sri Harsha Garapati

  26. DESIGN OF EXPERIMENTS Sri Harsha Garapati

  27. Results • ANSYS parametric design language (APDL) is developed to run all the combinations of the factors. • After each run, responses for sensitivity analysis are written to a text file. • Matlab Program is used to extract the LCDR,NMIRS and NMISS values from the text files and writes to a excel sheet. Sri Harsha Garapati

  28. LCDR LCDR can vary as mush as 20 to 50% depending up on the type of indenter LCDR depends only on the type of indenter Sri Harsha Garapati

  29. NMIRS differ as much as by 70% with boundary conditions for higher fiber volume fraction and differ as much as by 95% for lower fiber volume fraction. NMIRS NMIRS differ as much as by 32% with type of interphase for higher fiber volume fraction and differ as much as by 93% for lower fiber volume fraction. NMIRS differ as much as by 150% with type of interphase for higher fiber volume fraction and differ as much as by 190% for lower fiber volume fraction. Sri Harsha Garapati

  30. NMIRS Sri Harsha Garapati

  31. NMISS NMISS differ as much as by 170% with type of interphase for higher fiber volume fraction and differ as much as by 60% for lower fiber volume fraction. Sri Harsha Garapati

  32. NMISS Sri Harsha Garapati

  33. Comparison with Shear-Lag Models • Shear-lag models approximate the distributed loading on the entire fiber, but this assumption underestimates the shear modulus of the interphase by the order as much as 1000. Sri Harsha Garapati

  34. Conclusions • LCDR can differ by as much as 20 to 50% depending up on the type of distribution of load. • NMIRS could vary up to 95% depending up on the assumed or applied boundary conditions. • NMIRS could vary from 32 to 93% depending upon the thickness of interphase. • NMISS could differ by 170% depending up on the boundary conditions Sri Harsha Garapati

  35. Conclusions • The load-displacement curve is dependent only on type of load distribution. • The critical interfacial radial stress is mainly dependent on the fiber volume fraction, type of interphase, thickness of interphase and the boundary conditions. • The critical interfacial shear stress is mainly dependent on the fiber volume fraction and the boundary conditions. Sri Harsha Garapati

  36. Conclusions • Approximating indentor loading as distributed uniformly throughout the fiber can underestimate the extracted property of the shear modulus of the interphase by an order of as much as a 1000. Sri Harsha Garapati

  37. Questions ? Sri Harsha Garapati

  38. Thank You Sri Harsha Garapati

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